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Old 18th January 2005, 10:58 PM   #1
jered22 is offline jered22  United States
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Default The Golden Rule?

Has anyone ever heard of the Golden Rule in speaker box building? I heard something about this and the formula is supposed to be 0.6 x 1.0 x 1.6 I am not sure what the multiplier is but I figure these three numbers are the height/width/depth when multiplied by another number. Could someone please help me with this one. I am going to be building a home theater system and need to figure out what size box I am going to need. The big question is If I am going to be putting two Tang Band W3-881S into one enclosure what size does the inside measurments need to be for each speaker? If possible I would like to keep the depth around 4" and the enclosure taller than wider. Going for the slimmer look. Thanks for any advice that comes my way.

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Old 19th January 2005, 01:27 AM   #2
Sherman is offline Sherman  United States
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Default Re: The Golden Rule?

Quote:
Originally posted by jered22
... I heard something about this and the formula is supposed to be 0.6 x 1.0 x 1.6 I am not sure what the multiplier is but I figure these three numbers are the height/width/depth when multiplied by another number...
Jered22

It is the "Golden Ratio". When a speaker box is built with its dimensions in this ratio internal standing waves are (supposed to be) minimized. So the numbers themselves are the multipliers.

If your width for instance is 6 inches then the depth would be 10 inches and the height would be 16 inches. It actually doesn't matter with dimension is the height, width or depth.
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Old 19th January 2005, 01:41 AM   #3
jered22 is offline jered22  United States
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So if this is true and I was building a box for a 3" driver and I wanted my box to be 3" in depth the box size should be 3"x10"x13" ? Is this correct? or 4" in depth it would be 4"x10"x14"? It seems to easy as if I am doing it wrong.

I am looking for the smallest box possible without compromising sound response for the Tang Band W3-881S. I really need help! I am very new and don't understand the box dimensions. Please Help! I tried the freeware but that really does not help. I just need to know the internal cubic inches needed for one.

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Old 19th January 2005, 01:54 AM   #4
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No, the 3" driver looks like 3 x 5 x 8" and the 4" looks like 4 x 6.6 x 10" to me.
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Old 19th January 2005, 02:04 AM   #5
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Wouldn't it be better to use prime numbers for ratios?

:)ensen.
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Old 19th January 2005, 02:20 AM   #6
AndyN is offline AndyN  United States
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http://mathworld.wolfram.com/GoldenRectangle.html

The math can look a bit daunting, but if you note the parts about what Euclid did with geometry, you'll get a pretty good feel for it.

As others have said, make the length of a rectangle equal to 1.61 times it's side and you're on your way.

Dig up a copy of "The Power of Limits" by Gyorgy Doczi for a good time. It starts with the appearance of the divine ratio in nature and art, and goes outward from there.

How come math was never this fun / useful / interesting in school?
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Old 19th January 2005, 02:28 AM   #7
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Quote:
Originally posted by purplepeople
Wouldn't it be better to use prime numbers for ratios?

ensen.
Actually, not really. The idea behind the golden ratio is that it's irrational; it's not a proper fraction. The actual number is 1.61803... the formula to find it is (1+sqrrt(5))/2.

As far as why it's been thought of as a good idea to use in audio, I think that's because you might have a 500hz standing wave between two panels, but with that ratio you will not have a standing wave at 250 or 1000 hz between two other panels.

If your box is small enough that the smallest wavelength in its passband is greater than 4 times the longest internal dimension (say, corner to corner), you shouldn't have any trouble with internal standing waves. Another way to fight internal standing waves is to use trapezoids, so the walls aren't parallel. This prevents large flat areas from being of a constant equal distance.

Here's a site with more information about the golden ratio, but I think they over-hype it just a little bit.

http://goldennumber.net/

Other ways to fight standing waves include fibrous stuffing material (poly-fill from wal-mart) in a regular tapered box, or in a tapered terminated tube- like the B&W nautalus.

So, I think that's why (other than looks) that you hear about the golden ratio in speakers. If anyone has more info, I'd be eager to hear it
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Old 19th January 2005, 03:56 PM   #8
GM is offline GM  United States
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Quote:
So if this is true and I was building a box for a 3" driver and I wanted my box to be 3" in depth the box size should be 3"x10"x13" ? Is this correct? or 4" in depth it would be 4"x10"x14"? It seems to easy as if I am doing it wrong.
How can it be? Using 4" as the base: 4/0.618 = ~6.47" and ~6.47*1.618 = ~10.47", but you have to find the proper volume (Vb) required for whatever frequency response (FR) you want (alignment). If not, then you will have to figure out its dimensions using either a golden or acoustic ratio (there's a bunch of acceptable ones). Or do like most folks and make them whatever dims you want and use as much stuffing as required to make it sound good to you.
Quote:
The big question is If I am going to be putting two Tang Band W3-881S into one enclosure what size does the inside measurments need to be for each speaker? If possible I would like to keep the depth around 4" and the enclosure taller than wider.
Well, I assume you will be using a sub and will be setting these speakers to 'small', but even then they won't play very loud without audibly distorting. Anyway, assuming the 4" is o.d., making the inside dim 2.5" assuming 0.75" thick material, then using one of the other parts of the golden ratio, 2.5*1.618 = ~4.03", and since 0.67ft^3 is required (Vb) the long dim = (0.67*1728")/(2.5"*4.03") = 114.91", probably somewhat slimmer than you had in mind and definitely not a good idea due to the strong standing waves well above/beyond the ideal for this driver if a ML-TL.

So about all you can do if one dim is 2.5" is to multiply the longest internal dim you can tolerate by 2.5 (or other dim) and divide it into the Vb to find the width. Again, assuming a 0.75" thick baffle, the vent would be a 2" diameter hole. Add stuffing to 'taste'.

GM
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Old 19th January 2005, 04:07 PM   #9
GM is offline GM  United States
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So, I think that's why (other than looks) that you hear about the golden ratio in speakers. If anyone has more info, I'd be eager to hear it
No, this is pretty much it. With the exception of MJK's and a few other programs, they all assume the cab has a ~uniform particle density so the only way the cab will perform exactly as modeled is if it is a golden or acoustic ratio with the vent exiting the bottom and the driver positioned based on its acoustic resonant center. If you ignore the vent's impact on this, then it will always be near/at the cab's horizontal centerline.

GM
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Old 19th January 2005, 04:18 PM   #10
markp is offline markp  United States
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Actually, there are many 'golden ratios'. The idea behind them is that the product of all the dimensions is equal to 1. Notice that .6x1x1.6=1 and .8x1x1.25=1 and so on.
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